# simpson

From untb v1.3-3
by Robin S. Hankin

##### Simpson's diversity index

Simpson's diversity index

- Keywords
- math

##### Usage

`simpson(x)`

##### Arguments

- x
- Ecosystem vector; coerced to class
`count`

##### Details

Returns the Simpson index $D$: the probability that two randomly sampled individuals belong to different species. This is $$1-\sum_{i=1}^S\left(p_i\right)^2$$

where $p_i$ is the relative frequency of the $i^{\rm th}$ species

##### Note

Early versions of the *different*
individuals belong to different species

##### References

- S. P. Hubbell 2001.
The Unified Neutral Theory of Biodiversity . Princeton University Press. - F. He and X.-S. Hu 2005.
Hubbell's Fundamental Biodiversity Parameter and the Simpson Diversity Index . Ecology Letters, volume 8, pp386-390. doi:`10.1111/j.1461-0248.2005.00729.x`

- E. H. Simpson 1949.
Measurement of diversity . Nature, volume 163, p688

##### See Also

##### Examples

```
data(butterflies)
D <- simpson(butterflies)
theta <- optimal.prob(butterflies)*2*no.of.ind(butterflies)
#compare theta with D/(1-D) (should be roughly equal):
theta
D/(1-D)
```

*Documentation reproduced from package untb, version 1.3-3, License: GPL*

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